It was never said that Gozer's coming always had to herald the end of the world.
Gozer was supposed to be an ancient Sumerian demi-god that could summoned by it's followers. Gozer also had more than one incarnation. Louis spoke of Gozer the Traveller, which had pre-chosen forms it could appear as and wreak havoc:
“Gozer the Traveller will come in one of the pre-chosen forms. During the rectification of the Vuldronaii the Traveller came as a very large and moving Torb. Then of course in the third reconciliation of the last of the Meketrex supplicants they chose a new form for him, that of a Sloar. Many Shubs and Zuuls knew what it was to be roasted in the depths of the Sloar that day I can tell you.”
And Gozer the Traveller appeared in the form of the girl wearing bubblewrap on top of Dana's Apartment. But why did the Traveller disappear before ending the world? Obviously the Traveller was only an incarnation only powerful enough to cause severe damage to the enemies of the party who summoned it.
But Shandor (the architect of Dana's building) wished to bring Gozer the Destructor to Earth, in order to destroy it. The Destructor's form had to be chosen by those about to be annhilated (which is why Gozer took the form of the Stay Puft Marshmallow Man to destroy the Ghostbusters.) So The Destructor must be an incarnation of Gozer powerful enough to destroy the world (and by ancient Sumerian standards, that wouldn't be very hard, because the “world” 100,000 years ago wasn't very big by population standards!)
And since Gozer the Destructor wasn't mentioned by Louis, it leads one to believe that the Destructor had never appeared on Earth before, which is why the world was still around at the time of GB1.
A simple matter of getting your incarnations confused, young padawan.
—Ecto1A